Remove chicken from broth; cool slightly and remove the meat from bones, discarding bones and skin. Shred chicken into chunks and return to pot. Add the chicken base and noodles; reheat just to a boil. Remove from heat and stir in the cilantro leaves and lime juice.

To serve, ladle soup into bowls, top with a dollop of sour cream and pass the lime wedges and tortillas for accompaniment, as desired.